A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by ?
The range of temperature in degree Celsius is between 20°C and 25°C, i.e., 20 < C < 25.
Explanation
This question is similar to Example 12 in the textbook, but requires converting from Fahrenheit to Celsius instead of Celsius to Fahrenheit. The student needs to use the given formula F = (9/5)C + 32 and solve for C to find the equivalent Celsius range. The key steps involve rearranging the formula to express C in terms of F, then substituting the boundary values 68°F and 77°F.
Solution Steps
Step 1: Given that the solution must be kept between 68°F and 77°F, we write: 68 < F < 77
Step 2: Using the formula F = (9/5)C + 32, solve for C: F - 32 = (9/5)C, therefore C = (5/9)(F - 32)
Step 3: Substitute the boundary values: For F = 68: C = (5/9)(68 - 32) = (5/9)(36) = ()/9 = 180/9 = 20
Step 4: For F = 77: C = (5/9)(77 - 32) = (5/9)(45) = ()/9 = 225/9 = 25
Step 5: Therefore, the range in degree Celsius is: 20 < C < 25